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Choosing correct ratio from a situation

Choosing the correct ratio from a situation means selecting the trigonometric ratio that matches the given sides or the required unknown in a word problem.

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Student-friendly explanation

In applied questions, the diagram or description tells you which side is known and which side is needed. The correct ratio is not chosen by guesswork. It is chosen by matching the situation to opposite, adjacent, and hypotenuse with respect to the given angle.

How to write this in exams

  1. 1

    Start with the exact idea

    Choosing the correct ratio from a situation means selecting the trigonometric ratio that matches the given sides or the required unknown in a word problem.

  2. 2

    Then show how to use it

    1. Convert the situation into a right triangle. 2. Mark the angle of interest. 3. Identify known and unknown sides. 4. Pick the ratio that connects them directly. 5. Solve the equation.

  3. 3

    Add one concrete example

    If a ladder makes an angle with the ground and the height reached on the wall is needed, sine or tangent may be used depending on the sides given.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to use a ratio that includes an extra side and makes the equation longer than needed.

Definition

Choosing the correct ratio from a situation means selecting the trigonometric ratio that matches the given sides or the required unknown in a word problem.

Example

If a ladder makes an angle with the ground and the height reached on the wall is needed, sine or tangent may be used depending on the sides given.

Rule to remember

Match the known and required sides with the angle: sine uses opposite and hypotenuse, cosine uses adjacent and hypotenuse, tangent uses opposite and adjacent.

Memory hook

Choose the ratio by side match, not by memory alone.

Examples and method

Worked example

If a pole is vertical and the ground distance is known with the angle of elevation, tan can be used to connect height and base directly.

Method to apply

1. Convert the situation into a right triangle. 2. Mark the angle of interest. 3. Identify known and unknown sides. 4. Pick the ratio that connects them directly. 5. Solve the equation.

Diagram support

Draw the situation as a right triangle whenever possible. Mark the angle and label the given sides before choosing any ratio.

How CBSE asks it

CBSE may ask word problems on height and distance, ladder problems, angle of elevation, or choose-the-ratio questions from a diagram.

Avoid common mistakes

Common confusion

Students often choose a ratio only because it sounds familiar, not because it matches the sides in the question.

Common wrong answer

A common wrong answer is to use a ratio that includes an extra side and makes the equation longer than needed.

Exam tip

First decide the angle, then decide whether the question uses opposite, adjacent, or hypotenuse.

Quick check

A ladder problem gives the length of the ladder and the height reached on the wall. Which ratio is often most direct?

The most direct ratio is usually sine, because height is opposite the ground angle and the ladder is the hypotenuse. The exact choice still depends on the angle and the given sides.

Answer writing and exam use

1-mark answer

Choosing the correct ratio from a situation means selecting the trigonometric ratio that matches the given sides or the required unknown in a word problem.

2-mark answer

Choosing the correct ratio from a situation means selecting the trigonometric ratio that matches the given sides or the required unknown in a word problem. Match the known and required sides with the angle: sine uses opposite and hypotenuse, cosine uses adjacent and hypotenuse, tangent uses opposite and adjacent. If a ladder makes an angle with the ground and the height reached on the wall is needed, sine or tangent may be used depending on the sides given.

3-mark answer

In applied questions, the diagram or description tells you which side is known and which side is needed. The correct ratio is not chosen by guesswork. It is chosen by matching the situation to opposite, adjacent, and hypotenuse with respect to the given angle. Match the known and required sides with the angle: sine uses opposite and hypotenuse, cosine uses adjacent and hypotenuse, tangent uses opposite and adjacent. If a pole is vertical and the ground distance is known with the angle of elevation, tan can be used to connect height and base directly. CBSE may ask word problems on height and distance, ladder problems, angle of elevation, or choose-the-ratio questions from a diagram. A common wrong answer is to use a ratio that includes an extra side and makes the equation longer than needed.
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